Functions vs Non Functions

Recognizing functions A function has one output value for every input: f(x) = x2 f(x) = x3 f(x) = 3x x f(x) 3 6 9 12 15 x f(x) -2 4 -1 1 0 0 x f(x) -2 -8 -1 -1 0 0 1 8

Recognizing functions Let’s look at f(x) = √x 0 0 x f(x) √0 = 1 1 -1 √1 = 1 or -1 4 2 -2 √4 = or -2 2 The equation f(x) = √x is NOT a function because for every x value there are 2 possible f(x) values

Non Function f(x) = √x x f(x) 1 1 1 -1 4 2 4 -2

Vertical line test To decide if a graph shows a function, use a vertical line to see if there are 2 or more y-values for any given x-value If the vertical line crosses the graph in more than one place, it is not a function

Vertical line test This is NOT a function

examples Identify which graphs show a function No Yes Yes No No Yes

try! Which graphs represent functions? Yes Yes No No © 2013 Meredith S. Moody Yes No Yes No